Two classes of risk model with diffusion and multiple thresholds: the discounted dividends

Year 2019, Volume: 48 Issue: 1, 200 - 212, 01.02.2019

Wuyuan Jiang

Abstract

In this paper, we consider the present value of total dividends until ruin in a perturbed risk model with two independent classes of risks under multiple thresholds, in which both of the two inter-claim times have phase-type distributions. We obtain the integro-differential equations for the moment-generating function and the $r$th moment of discounted dividend payments. Explicit expressions for the expectation of discounted dividend payments are derived if the two classes claim amount
distributions both belong to the rational family.

Keywords

Two classes of claims, Diffusion process, Dividend payments, Multiple thresholds, Phase-type distribution

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